TSTP Solution File: SYN056^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN056^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:33:55 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN056^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 14:56:23 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % (17842)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (17848)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.36 % (17847)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.36 % (17849)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.36 % (17844)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.36 % Exception at run slice level
% 0.12/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % (17846)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.36 % Exception at run slice level
% 0.12/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % (17846)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.36 % Exception at run slice level
% 0.12/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % (17845)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.12/0.37 % (17848)First to succeed.
% 0.12/0.37 % (17845)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % (17848)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17842"
% 0.12/0.37 % (17848)Refutation found. Thanks to Tanya!
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% 0.12/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.37 thf(func_def_0, type, cR: $i > $o).
% 0.12/0.37 thf(func_def_1, type, cP: $i > $o).
% 0.12/0.37 thf(func_def_2, type, cS: $i > $o).
% 0.12/0.37 thf(func_def_3, type, cQ: $i > $o).
% 0.12/0.37 thf(func_def_7, type, sP0: $o).
% 0.12/0.37 thf(func_def_13, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.12/0.37 thf(func_def_14, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.12/0.37 thf(func_def_15, type, vAND: $o > $o > $o).
% 0.12/0.37 thf(func_def_16, type, vOR: $o > $o > $o).
% 0.12/0.37 thf(func_def_17, type, vIMP: $o > $o > $o).
% 0.12/0.37 thf(func_def_18, type, vNOT: $o > $o).
% 0.12/0.37 thf(func_def_19, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.12/0.37 thf(f185,plain,(
% 0.12/0.37 $false),
% 0.12/0.37 inference(avatar_sat_refutation,[],[f38,f43,f47,f52,f57,f61,f65,f69,f77,f85,f127,f129,f146,f152,f154,f161,f166,f184])).
% 0.12/0.37 thf(f184,plain,(
% 0.12/0.37 spl5_10 | ~spl5_7 | ~spl5_8),
% 0.12/0.37 inference(avatar_split_clause,[],[f183,f63,f59,f71])).
% 0.12/0.37 thf(f71,plain,(
% 0.12/0.37 spl5_10 <=> ! [X5] : ($true != vAPP($i,$o,cQ,X5))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_10])])).
% 0.12/0.37 thf(f59,plain,(
% 0.12/0.37 spl5_7 <=> ! [X1] : ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cQ,X1) != $true))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_7])])).
% 0.12/0.37 thf(f63,plain,(
% 0.12/0.37 spl5_8 <=> ! [X3] : (($true != vAPP($i,$o,cS,X3)) | ($true != vAPP($i,$o,cQ,X3)))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_8])])).
% 0.12/0.37 thf(f183,plain,(
% 0.12/0.37 ( ! [X3 : $i] : (($true != vAPP($i,$o,cQ,X3))) ) | (~spl5_7 | ~spl5_8)),
% 0.12/0.37 inference(subsumption_resolution,[],[f64,f60])).
% 0.12/0.37 thf(f60,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((vAPP($i,$o,cQ,X1) != $true) | (vAPP($i,$o,cS,X1) = $true)) ) | ~spl5_7),
% 0.12/0.37 inference(avatar_component_clause,[],[f59])).
% 0.12/0.37 thf(f64,plain,(
% 0.12/0.37 ( ! [X3 : $i] : (($true != vAPP($i,$o,cS,X3)) | ($true != vAPP($i,$o,cQ,X3))) ) | ~spl5_8),
% 0.12/0.37 inference(avatar_component_clause,[],[f63])).
% 0.12/0.37 thf(f166,plain,(
% 0.12/0.37 ~spl5_3 | ~spl5_10),
% 0.12/0.37 inference(avatar_contradiction_clause,[],[f165])).
% 0.12/0.37 thf(f165,plain,(
% 0.12/0.37 $false | (~spl5_3 | ~spl5_10)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f162])).
% 0.12/0.37 thf(f162,plain,(
% 0.12/0.37 ($true != $true) | (~spl5_3 | ~spl5_10)),
% 0.12/0.37 inference(superposition,[],[f72,f42])).
% 0.12/0.37 thf(f42,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cQ,sK1)) | ~spl5_3),
% 0.12/0.37 inference(avatar_component_clause,[],[f40])).
% 0.12/0.37 thf(f40,plain,(
% 0.12/0.37 spl5_3 <=> ($true = vAPP($i,$o,cQ,sK1))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_3])])).
% 0.12/0.37 thf(f72,plain,(
% 0.12/0.37 ( ! [X5 : $i] : (($true != vAPP($i,$o,cQ,X5))) ) | ~spl5_10),
% 0.12/0.37 inference(avatar_component_clause,[],[f71])).
% 0.12/0.37 thf(f161,plain,(
% 0.12/0.37 ~spl5_11 | ~spl5_12),
% 0.12/0.37 inference(avatar_contradiction_clause,[],[f160])).
% 0.12/0.37 thf(f160,plain,(
% 0.12/0.37 $false | (~spl5_11 | ~spl5_12)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f157])).
% 0.12/0.37 thf(f157,plain,(
% 0.12/0.37 ($true != $true) | (~spl5_11 | ~spl5_12)),
% 0.12/0.37 inference(superposition,[],[f80,f76])).
% 0.12/0.37 thf(f76,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cP,sK3)) | ~spl5_11),
% 0.12/0.37 inference(avatar_component_clause,[],[f74])).
% 0.12/0.37 thf(f74,plain,(
% 0.12/0.37 spl5_11 <=> ($true = vAPP($i,$o,cP,sK3))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_11])])).
% 0.12/0.37 thf(f80,plain,(
% 0.12/0.37 ( ! [X7 : $i] : (($true != vAPP($i,$o,cP,X7))) ) | ~spl5_12),
% 0.12/0.37 inference(avatar_component_clause,[],[f79])).
% 0.12/0.37 thf(f79,plain,(
% 0.12/0.37 spl5_12 <=> ! [X7] : ($true != vAPP($i,$o,cP,X7))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_12])])).
% 0.12/0.37 thf(f154,plain,(
% 0.12/0.37 spl5_12 | ~spl5_4 | ~spl5_9),
% 0.12/0.37 inference(avatar_split_clause,[],[f153,f67,f45,f79])).
% 0.12/0.37 thf(f45,plain,(
% 0.12/0.37 spl5_4 <=> ! [X1] : (($true = vAPP($i,$o,cR,X1)) | ($true != vAPP($i,$o,cP,X1)))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_4])])).
% 0.12/0.37 thf(f67,plain,(
% 0.12/0.37 spl5_9 <=> ! [X2] : (($true != vAPP($i,$o,cR,X2)) | ($true != vAPP($i,$o,cP,X2)))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_9])])).
% 0.12/0.37 thf(f153,plain,(
% 0.12/0.37 ( ! [X2 : $i] : (($true != vAPP($i,$o,cP,X2))) ) | (~spl5_4 | ~spl5_9)),
% 0.12/0.37 inference(subsumption_resolution,[],[f68,f46])).
% 0.12/0.37 thf(f46,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (($true != vAPP($i,$o,cP,X1)) | ($true = vAPP($i,$o,cR,X1))) ) | ~spl5_4),
% 0.12/0.37 inference(avatar_component_clause,[],[f45])).
% 0.12/0.37 thf(f68,plain,(
% 0.12/0.37 ( ! [X2 : $i] : (($true != vAPP($i,$o,cR,X2)) | ($true != vAPP($i,$o,cP,X2))) ) | ~spl5_9),
% 0.12/0.37 inference(avatar_component_clause,[],[f67])).
% 0.12/0.37 thf(f152,plain,(
% 0.12/0.37 spl5_2 | ~spl5_3 | ~spl5_7),
% 0.12/0.37 inference(avatar_contradiction_clause,[],[f151])).
% 0.12/0.37 thf(f151,plain,(
% 0.12/0.37 $false | (spl5_2 | ~spl5_3 | ~spl5_7)),
% 0.12/0.37 inference(subsumption_resolution,[],[f150,f37])).
% 0.12/0.37 thf(f37,plain,(
% 0.12/0.37 ($true != vAPP($i,$o,cS,sK1)) | spl5_2),
% 0.12/0.37 inference(avatar_component_clause,[],[f35])).
% 0.12/0.37 thf(f35,plain,(
% 0.12/0.37 spl5_2 <=> ($true = vAPP($i,$o,cS,sK1))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_2])])).
% 0.12/0.37 thf(f150,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cS,sK1)) | (~spl5_3 | ~spl5_7)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f149])).
% 0.12/0.37 thf(f149,plain,(
% 0.12/0.37 ($true != $true) | ($true = vAPP($i,$o,cS,sK1)) | (~spl5_3 | ~spl5_7)),
% 0.12/0.37 inference(superposition,[],[f60,f42])).
% 0.12/0.37 thf(f146,plain,(
% 0.12/0.37 spl5_5 | ~spl5_4 | ~spl5_6),
% 0.12/0.37 inference(avatar_split_clause,[],[f142,f54,f45,f49])).
% 0.12/0.37 thf(f49,plain,(
% 0.12/0.37 spl5_5 <=> ($true = vAPP($i,$o,cR,sK2))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_5])])).
% 0.12/0.37 thf(f54,plain,(
% 0.12/0.37 spl5_6 <=> ($true = vAPP($i,$o,cP,sK2))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_6])])).
% 0.12/0.37 thf(f142,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cR,sK2)) | (~spl5_4 | ~spl5_6)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f137])).
% 0.12/0.37 thf(f137,plain,(
% 0.12/0.37 ($true != $true) | ($true = vAPP($i,$o,cR,sK2)) | (~spl5_4 | ~spl5_6)),
% 0.12/0.37 inference(superposition,[],[f46,f56])).
% 0.12/0.37 thf(f56,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cP,sK2)) | ~spl5_6),
% 0.12/0.37 inference(avatar_component_clause,[],[f54])).
% 0.12/0.37 thf(f129,plain,(
% 0.12/0.37 ~spl5_10 | ~spl5_13),
% 0.12/0.37 inference(avatar_contradiction_clause,[],[f128])).
% 0.12/0.37 thf(f128,plain,(
% 0.12/0.37 $false | (~spl5_10 | ~spl5_13)),
% 0.12/0.37 inference(subsumption_resolution,[],[f84,f72])).
% 0.12/0.37 thf(f84,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cQ,sK4)) | ~spl5_13),
% 0.12/0.37 inference(avatar_component_clause,[],[f82])).
% 0.12/0.37 thf(f82,plain,(
% 0.12/0.37 spl5_13 <=> ($true = vAPP($i,$o,cQ,sK4))),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_13])])).
% 0.12/0.37 thf(f127,plain,(
% 0.12/0.37 ~spl5_6 | ~spl5_12),
% 0.12/0.37 inference(avatar_contradiction_clause,[],[f126])).
% 0.12/0.37 thf(f126,plain,(
% 0.12/0.37 $false | (~spl5_6 | ~spl5_12)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f123])).
% 0.12/0.37 thf(f123,plain,(
% 0.12/0.37 ($true != $true) | (~spl5_6 | ~spl5_12)),
% 0.12/0.37 inference(superposition,[],[f80,f56])).
% 0.12/0.37 thf(f85,plain,(
% 0.12/0.37 spl5_12 | spl5_13),
% 0.12/0.37 inference(avatar_split_clause,[],[f23,f82,f79])).
% 0.12/0.37 thf(f23,plain,(
% 0.12/0.37 ( ! [X7 : $i] : (($true = vAPP($i,$o,cQ,sK4)) | ($true != vAPP($i,$o,cP,X7))) )),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f19,plain,(
% 0.12/0.37 (((($true != vAPP($i,$o,cR,sK2)) & ($true = vAPP($i,$o,cP,sK2))) & ! [X1] : ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cQ,X1) != $true))) | ($true = sP0)) & ! [X2,X3] : (((($true = vAPP($i,$o,cR,X2)) | ($true != vAPP($i,$o,cS,X3))) & (($true = vAPP($i,$o,cS,X3)) | ($true != vAPP($i,$o,cR,X2)))) | ($true != vAPP($i,$o,cQ,X3)) | ($true != vAPP($i,$o,cP,X2))) & (($true = vAPP($i,$o,cP,sK3)) | ! [X5] : ($true != vAPP($i,$o,cQ,X5))) & (($true = vAPP($i,$o,cQ,sK4)) | ! [X7] : ($true != vAPP($i,$o,cP,X7)))),
% 0.12/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f15,f18,f17,f16])).
% 0.12/0.37 thf(f16,plain,(
% 0.12/0.37 ? [X0] : ((vAPP($i,$o,cR,X0) != $true) & (vAPP($i,$o,cP,X0) = $true)) => (($true != vAPP($i,$o,cR,sK2)) & ($true = vAPP($i,$o,cP,sK2)))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f17,plain,(
% 0.12/0.37 ? [X4] : ($true = vAPP($i,$o,cP,X4)) => ($true = vAPP($i,$o,cP,sK3))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f18,plain,(
% 0.12/0.37 ? [X6] : ($true = vAPP($i,$o,cQ,X6)) => ($true = vAPP($i,$o,cQ,sK4))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f15,plain,(
% 0.12/0.37 ((? [X0] : ((vAPP($i,$o,cR,X0) != $true) & (vAPP($i,$o,cP,X0) = $true)) & ! [X1] : ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cQ,X1) != $true))) | ($true = sP0)) & ! [X2,X3] : (((($true = vAPP($i,$o,cR,X2)) | ($true != vAPP($i,$o,cS,X3))) & (($true = vAPP($i,$o,cS,X3)) | ($true != vAPP($i,$o,cR,X2)))) | ($true != vAPP($i,$o,cQ,X3)) | ($true != vAPP($i,$o,cP,X2))) & (? [X4] : ($true = vAPP($i,$o,cP,X4)) | ! [X5] : ($true != vAPP($i,$o,cQ,X5))) & (? [X6] : ($true = vAPP($i,$o,cQ,X6)) | ! [X7] : ($true != vAPP($i,$o,cP,X7)))),
% 0.12/0.37 inference(rectify,[],[f10])).
% 0.12/0.37 thf(f10,plain,(
% 0.12/0.37 ((? [X7] : (($true != vAPP($i,$o,cR,X7)) & ($true = vAPP($i,$o,cP,X7))) & ! [X6] : (($true = vAPP($i,$o,cS,X6)) | ($true != vAPP($i,$o,cQ,X6)))) | ($true = sP0)) & ! [X0,X1] : ((((vAPP($i,$o,cR,X0) = $true) | (vAPP($i,$o,cS,X1) != $true)) & ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cR,X0) != $true))) | (vAPP($i,$o,cQ,X1) != $true) | (vAPP($i,$o,cP,X0) != $true)) & (? [X3] : ($true = vAPP($i,$o,cP,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (? [X5] : ($true = vAPP($i,$o,cQ,X5)) | ! [X4] : ($true != vAPP($i,$o,cP,X4)))),
% 0.12/0.37 inference(definition_folding,[],[f8,f9])).
% 0.12/0.37 thf(f9,plain,(
% 0.12/0.37 (? [X9] : (($true != vAPP($i,$o,cS,X9)) & ($true = vAPP($i,$o,cQ,X9))) & ! [X8] : (($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cP,X8)))) | ~($true = sP0)),
% 0.12/0.37 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.12/0.37 thf(f8,plain,(
% 0.12/0.37 ((? [X7] : (($true != vAPP($i,$o,cR,X7)) & ($true = vAPP($i,$o,cP,X7))) & ! [X6] : (($true = vAPP($i,$o,cS,X6)) | ($true != vAPP($i,$o,cQ,X6)))) | (? [X9] : (($true != vAPP($i,$o,cS,X9)) & ($true = vAPP($i,$o,cQ,X9))) & ! [X8] : (($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cP,X8))))) & ! [X0,X1] : ((((vAPP($i,$o,cR,X0) = $true) | (vAPP($i,$o,cS,X1) != $true)) & ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cR,X0) != $true))) | (vAPP($i,$o,cQ,X1) != $true) | (vAPP($i,$o,cP,X0) != $true)) & (? [X3] : ($true = vAPP($i,$o,cP,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (? [X5] : ($true = vAPP($i,$o,cQ,X5)) | ! [X4] : ($true != vAPP($i,$o,cP,X4)))),
% 0.12/0.37 inference(flattening,[],[f7])).
% 0.12/0.37 thf(f7,plain,(
% 0.12/0.37 ((? [X7] : (($true != vAPP($i,$o,cR,X7)) & ($true = vAPP($i,$o,cP,X7))) & ! [X6] : (($true = vAPP($i,$o,cS,X6)) | ($true != vAPP($i,$o,cQ,X6)))) | (? [X9] : (($true != vAPP($i,$o,cS,X9)) & ($true = vAPP($i,$o,cQ,X9))) & ! [X8] : (($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cP,X8))))) & (! [X0,X1] : ((((vAPP($i,$o,cR,X0) = $true) | (vAPP($i,$o,cS,X1) != $true)) & ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cR,X0) != $true))) | ((vAPP($i,$o,cQ,X1) != $true) | (vAPP($i,$o,cP,X0) != $true))) & (? [X3] : ($true = vAPP($i,$o,cP,X3)) | ! [X2] : ($true != vAPP($i,$o,cQ,X2))) & (? [X5] : ($true = vAPP($i,$o,cQ,X5)) | ! [X4] : ($true != vAPP($i,$o,cP,X4))))),
% 0.12/0.37 inference(ennf_transformation,[],[f6])).
% 0.12/0.37 thf(f6,plain,(
% 0.12/0.37 ~((! [X0,X1] : (((vAPP($i,$o,cQ,X1) = $true) & (vAPP($i,$o,cP,X0) = $true)) => (((vAPP($i,$o,cS,X1) = $true) => (vAPP($i,$o,cR,X0) = $true)) & ((vAPP($i,$o,cR,X0) = $true) => (vAPP($i,$o,cS,X1) = $true)))) & (? [X2] : ($true = vAPP($i,$o,cQ,X2)) => ? [X3] : ($true = vAPP($i,$o,cP,X3))) & (? [X4] : ($true = vAPP($i,$o,cP,X4)) => ? [X5] : ($true = vAPP($i,$o,cQ,X5)))) => ((! [X6] : (($true = vAPP($i,$o,cQ,X6)) => ($true = vAPP($i,$o,cS,X6))) => ! [X7] : (($true = vAPP($i,$o,cP,X7)) => ($true = vAPP($i,$o,cR,X7)))) & (! [X8] : (($true = vAPP($i,$o,cP,X8)) => ($true = vAPP($i,$o,cR,X8))) => ! [X9] : (($true = vAPP($i,$o,cQ,X9)) => ($true = vAPP($i,$o,cS,X9))))))),
% 0.12/0.37 inference(fool_elimination,[],[f5])).
% 0.12/0.37 thf(f5,plain,(
% 0.12/0.37 ~((! [X0,X1] : ((vAPP($i,$o,cQ,X1) & vAPP($i,$o,cP,X0)) => ((vAPP($i,$o,cS,X1) => vAPP($i,$o,cR,X0)) & (vAPP($i,$o,cR,X0) => vAPP($i,$o,cS,X1)))) & (? [X2] : vAPP($i,$o,cQ,X2) => ? [X3] : vAPP($i,$o,cP,X3)) & (? [X4] : vAPP($i,$o,cP,X4) => ? [X5] : vAPP($i,$o,cQ,X5))) => ((! [X6] : (vAPP($i,$o,cQ,X6) => vAPP($i,$o,cS,X6)) => ! [X7] : (vAPP($i,$o,cP,X7) => vAPP($i,$o,cR,X7))) & (! [X8] : (vAPP($i,$o,cP,X8) => vAPP($i,$o,cR,X8)) => ! [X9] : (vAPP($i,$o,cQ,X9) => vAPP($i,$o,cS,X9)))))),
% 0.12/0.37 inference(rectify,[],[f2])).
% 0.12/0.37 thf(f2,negated_conjecture,(
% 0.12/0.37 ~((! [X0,X1] : ((vAPP($i,$o,cQ,X1) & vAPP($i,$o,cP,X0)) => ((vAPP($i,$o,cS,X1) => vAPP($i,$o,cR,X0)) & (vAPP($i,$o,cR,X0) => vAPP($i,$o,cS,X1)))) & (? [X0] : vAPP($i,$o,cQ,X0) => ? [X0] : vAPP($i,$o,cP,X0)) & (? [X0] : vAPP($i,$o,cP,X0) => ? [X0] : vAPP($i,$o,cQ,X0))) => ((! [X0] : (vAPP($i,$o,cQ,X0) => vAPP($i,$o,cS,X0)) => ! [X0] : (vAPP($i,$o,cP,X0) => vAPP($i,$o,cR,X0))) & (! [X0] : (vAPP($i,$o,cP,X0) => vAPP($i,$o,cR,X0)) => ! [X0] : (vAPP($i,$o,cQ,X0) => vAPP($i,$o,cS,X0)))))),
% 0.12/0.37 inference(negated_conjecture,[],[f1])).
% 0.12/0.37 thf(f1,conjecture,(
% 0.12/0.37 (! [X0,X1] : ((vAPP($i,$o,cQ,X1) & vAPP($i,$o,cP,X0)) => ((vAPP($i,$o,cS,X1) => vAPP($i,$o,cR,X0)) & (vAPP($i,$o,cR,X0) => vAPP($i,$o,cS,X1)))) & (? [X0] : vAPP($i,$o,cQ,X0) => ? [X0] : vAPP($i,$o,cP,X0)) & (? [X0] : vAPP($i,$o,cP,X0) => ? [X0] : vAPP($i,$o,cQ,X0))) => ((! [X0] : (vAPP($i,$o,cQ,X0) => vAPP($i,$o,cS,X0)) => ! [X0] : (vAPP($i,$o,cP,X0) => vAPP($i,$o,cR,X0))) & (! [X0] : (vAPP($i,$o,cP,X0) => vAPP($i,$o,cR,X0)) => ! [X0] : (vAPP($i,$o,cQ,X0) => vAPP($i,$o,cS,X0))))),
% 0.12/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL26)).
% 0.12/0.37 thf(f77,plain,(
% 0.12/0.37 spl5_10 | spl5_11),
% 0.12/0.37 inference(avatar_split_clause,[],[f24,f74,f71])).
% 0.12/0.37 thf(f24,plain,(
% 0.12/0.37 ( ! [X5 : $i] : (($true = vAPP($i,$o,cP,sK3)) | ($true != vAPP($i,$o,cQ,X5))) )),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f69,plain,(
% 0.12/0.37 spl5_9 | spl5_7),
% 0.12/0.37 inference(avatar_split_clause,[],[f25,f59,f67])).
% 0.12/0.37 thf(f25,plain,(
% 0.12/0.37 ( ! [X2 : $i,X3 : $i] : (($true = vAPP($i,$o,cS,X3)) | ($true != vAPP($i,$o,cR,X2)) | ($true != vAPP($i,$o,cQ,X3)) | ($true != vAPP($i,$o,cP,X2))) )),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f65,plain,(
% 0.12/0.37 spl5_8 | spl5_4),
% 0.12/0.37 inference(avatar_split_clause,[],[f26,f45,f63])).
% 0.12/0.37 thf(f26,plain,(
% 0.12/0.37 ( ! [X2 : $i,X3 : $i] : (($true = vAPP($i,$o,cR,X2)) | ($true != vAPP($i,$o,cS,X3)) | ($true != vAPP($i,$o,cQ,X3)) | ($true != vAPP($i,$o,cP,X2))) )),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f61,plain,(
% 0.12/0.37 spl5_1 | spl5_7),
% 0.12/0.37 inference(avatar_split_clause,[],[f27,f59,f31])).
% 0.12/0.37 thf(f31,plain,(
% 0.12/0.37 spl5_1 <=> ($true = sP0)),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl5_1])])).
% 0.12/0.37 thf(f27,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((vAPP($i,$o,cS,X1) = $true) | (vAPP($i,$o,cQ,X1) != $true) | ($true = sP0)) )),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f57,plain,(
% 0.12/0.37 spl5_1 | spl5_6),
% 0.12/0.37 inference(avatar_split_clause,[],[f28,f54,f31])).
% 0.12/0.37 thf(f28,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cP,sK2)) | ($true = sP0)),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f52,plain,(
% 0.12/0.37 spl5_1 | ~spl5_5),
% 0.12/0.37 inference(avatar_split_clause,[],[f29,f49,f31])).
% 0.12/0.37 thf(f29,plain,(
% 0.12/0.37 ($true != vAPP($i,$o,cR,sK2)) | ($true = sP0)),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f47,plain,(
% 0.12/0.37 ~spl5_1 | spl5_4),
% 0.12/0.37 inference(avatar_split_clause,[],[f20,f45,f31])).
% 0.12/0.37 thf(f20,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (($true = vAPP($i,$o,cR,X1)) | ($true != vAPP($i,$o,cP,X1)) | ($true != sP0)) )),
% 0.12/0.37 inference(cnf_transformation,[],[f14])).
% 0.12/0.37 thf(f14,plain,(
% 0.12/0.37 ((($true != vAPP($i,$o,cS,sK1)) & ($true = vAPP($i,$o,cQ,sK1))) & ! [X1] : (($true = vAPP($i,$o,cR,X1)) | ($true != vAPP($i,$o,cP,X1)))) | ($true != sP0)),
% 0.12/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f12,f13])).
% 0.12/0.37 thf(f13,plain,(
% 0.12/0.37 ? [X0] : ((vAPP($i,$o,cS,X0) != $true) & (vAPP($i,$o,cQ,X0) = $true)) => (($true != vAPP($i,$o,cS,sK1)) & ($true = vAPP($i,$o,cQ,sK1)))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f12,plain,(
% 0.12/0.37 (? [X0] : ((vAPP($i,$o,cS,X0) != $true) & (vAPP($i,$o,cQ,X0) = $true)) & ! [X1] : (($true = vAPP($i,$o,cR,X1)) | ($true != vAPP($i,$o,cP,X1)))) | ($true != sP0)),
% 0.12/0.37 inference(rectify,[],[f11])).
% 0.12/0.37 thf(f11,plain,(
% 0.12/0.37 (? [X9] : (($true != vAPP($i,$o,cS,X9)) & ($true = vAPP($i,$o,cQ,X9))) & ! [X8] : (($true = vAPP($i,$o,cR,X8)) | ($true != vAPP($i,$o,cP,X8)))) | ($true != sP0)),
% 0.12/0.37 inference(nnf_transformation,[],[f9])).
% 0.12/0.37 thf(f43,plain,(
% 0.12/0.37 ~spl5_1 | spl5_3),
% 0.12/0.37 inference(avatar_split_clause,[],[f21,f40,f31])).
% 0.12/0.37 thf(f21,plain,(
% 0.12/0.37 ($true = vAPP($i,$o,cQ,sK1)) | ($true != sP0)),
% 0.12/0.37 inference(cnf_transformation,[],[f14])).
% 0.12/0.37 thf(f38,plain,(
% 0.12/0.37 ~spl5_1 | ~spl5_2),
% 0.12/0.37 inference(avatar_split_clause,[],[f22,f35,f31])).
% 0.12/0.37 thf(f22,plain,(
% 0.12/0.37 ($true != vAPP($i,$o,cS,sK1)) | ($true != sP0)),
% 0.12/0.37 inference(cnf_transformation,[],[f14])).
% 0.12/0.37 % SZS output end Proof for theBenchmark
% 0.12/0.37 % (17848)------------------------------
% 0.12/0.37 % (17848)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.37 % (17848)Termination reason: Refutation
% 0.12/0.37
% 0.12/0.37 % (17848)Memory used [KB]: 860
% 0.12/0.37 % (17848)Time elapsed: 0.008 s
% 0.12/0.37 % (17848)Instructions burned: 12 (million)
% 0.12/0.37 % (17842)Success in time 0.02 s
%------------------------------------------------------------------------------